Bazant Z.P., Le J.-L. Probabilistic Mechanics of Quasibrittle Structures: Strength, Lifetime, and Size Effect

Cambridge University Press, UK, 2017. — 317 p. — ISBN10: 1107151708.Quasibrittle (or brittle heterogeneous) materials are becoming increasingly important for modern engineering. They include concretes, rocks, fiber composites, tough ceramics, sea ice, bone, wood, stiff soils, rigid foams, glass, dental and biomaterials, as well as all brittle materials on the micro or nano scale. Their salient feature is that the fracture process zone size is non-negligible compared to the structural dimensions. This causes intricate energetic and statistical size effects and leads to size-dependent probability distribution of strength, transitional between Gaussian and Weibullian. The ensuing difficult challenges for safe design are vanquished in this book, which features a rigorous theory with detailed derivations yet no superfluous mathematical sophistication; extensive experimental verifications; and realistic approximations for design. A wide range of subjects is covered, including probabilistic fracture kinetics at nanoscale, multiscale transition, statistics of structural strength and lifetime, size effect, reliability indices, safety factors, and ramification to gate dielectrics breakdown.Review of Classical Statistical Theory of Structural Strength and Structural Safety, and of Statistics Fundamentals
Review of Fracture Mechanics and Deterministic Size Effect in Quasibrittle Structures
Failure Statistics of Nanoscale Structures
Nano–Macroscale Bridging of Probability Distributions of Static and Fatigue Strengths
Multiscale Modeling of Fracture Kinetics and Size Effect under Static and Cyclic Fatigue
Size Effect on Probability Distributions of Strength and Lifetime of Quasibrittle Structures
Computation of Probability Distributions of Structural Strength and Lifetime
Indirect Determination of Strength Statistics of Quasibrittle Structures
Statistical Distribution and Size Effect on Residual Strength after Sustained Load
Size Effect on Reliability Indices and Safety Factors
Crack Length Effect on Scaling of Structural Strength and Type 1 to 2 Transition
Effect of Stress Singularities on Scaling of Structural Strength
Lifetime of High-k Gate Dielectrics and Analogy with Failure Statistics of Quasibrittle Structures
Appendixes
Power-Law Scaling of Boundary Value Problems
Proof of Transitional Size Effects of Types 1 and 2 by Dimensional Analysis and Asymptotic Matching up to Second Order 260
Proof of Small-Size Asymptotics of Cohesive Crack Model up to Second Order